Step | Hyp | Ref
| Expression |
1 | | df-op 4566 |
. 2
Proj1 Proj2
Proj1
Phi
Proj2
Phi 0c |
2 | | df-proj1 4567 |
. . . . . . 7
Proj1 Phi |
3 | 2 | rexeqi 2812 |
. . . . . 6
Proj1
Phi
Phi
Phi |
4 | | phieq 4570 |
. . . . . . . 8
Phi Phi
|
5 | 4 | eleq1d 2419 |
. . . . . . 7
Phi Phi |
6 | 5 | rexab 2999 |
. . . . . 6
Phi Phi Phi Phi |
7 | | ancom 437 |
. . . . . . . . 9
Phi Phi Phi
Phi |
8 | | eleq1 2413 |
. . . . . . . . . 10
Phi Phi |
9 | 8 | pm5.32i 618 |
. . . . . . . . 9
Phi Phi Phi |
10 | 7, 9 | bitr4i 243 |
. . . . . . . 8
Phi Phi Phi
|
11 | 10 | exbii 1582 |
. . . . . . 7
Phi
Phi
Phi |
12 | | 19.41v 1901 |
. . . . . . 7
Phi
Phi |
13 | | ancom 437 |
. . . . . . 7
Phi
Phi |
14 | 11, 12, 13 | 3bitri 262 |
. . . . . 6
Phi
Phi
Phi |
15 | 3, 6, 14 | 3bitri 262 |
. . . . 5
Proj1
Phi
Phi |
16 | 15 | abbii 2465 |
. . . 4
Proj1 Phi Phi
|
17 | | df-rab 2623 |
. . . 4
Phi
Phi |
18 | 16, 17 | eqtr4i 2376 |
. . 3
Proj1 Phi Phi |
19 | | df-proj2 4568 |
. . . . . . 7
Proj2 Phi 0c |
20 | 19 | rexeqi 2812 |
. . . . . 6
Proj2
Phi 0c
Phi 0c
Phi 0c |
21 | 4 | uneq1d 3417 |
. . . . . . . 8
Phi 0c
Phi 0c |
22 | 21 | eleq1d 2419 |
. . . . . . 7
Phi 0c Phi 0c |
23 | 22 | rexab 2999 |
. . . . . 6
Phi 0c
Phi 0c
Phi 0c
Phi 0c |
24 | | ancom 437 |
. . . . . . . . 9
Phi 0c
Phi 0c Phi 0c Phi 0c |
25 | | eleq1 2413 |
. . . . . . . . . 10
Phi 0c Phi 0c |
26 | 25 | pm5.32i 618 |
. . . . . . . . 9
Phi
0c Phi 0c
Phi 0c
|
27 | 24, 26 | bitr4i 243 |
. . . . . . . 8
Phi 0c
Phi 0c Phi 0c
|
28 | 27 | exbii 1582 |
. . . . . . 7
Phi 0c Phi 0c
Phi 0c
|
29 | | 19.41v 1901 |
. . . . . . 7
Phi 0c
Phi 0c
|
30 | | ancom 437 |
. . . . . . 7
Phi 0c
Phi 0c |
31 | 28, 29, 30 | 3bitri 262 |
. . . . . 6
Phi 0c Phi 0c
Phi 0c |
32 | 20, 23, 31 | 3bitri 262 |
. . . . 5
Proj2
Phi 0c
Phi 0c |
33 | 32 | abbii 2465 |
. . . 4
Proj2 Phi 0c
Phi 0c |
34 | | df-rab 2623 |
. . . 4
Phi 0c Phi 0c |
35 | 33, 34 | eqtr4i 2376 |
. . 3
Proj2 Phi 0c
Phi 0c |
36 | 18, 35 | uneq12i 3416 |
. 2
Proj1
Phi
Proj2
Phi 0c Phi Phi 0c |
37 | | unrab 3526 |
. . 3
Phi Phi 0c Phi Phi 0c |
38 | | rabid2 2788 |
. . . 4
Phi
Phi 0c
Phi
Phi 0c |
39 | | vex 2862 |
. . . . . . 7
|
40 | 39 | phiall 4618 |
. . . . . 6
Phi Phi 0c |
41 | | 19.43 1605 |
. . . . . 6
Phi
Phi 0c
Phi
Phi 0c |
42 | 40, 41 | mpbi 199 |
. . . . 5
Phi
Phi 0c |
43 | 42 | a1i 10 |
. . . 4
Phi
Phi 0c |
44 | 38, 43 | mprgbir 2684 |
. . 3
Phi Phi 0c |
45 | 37, 44 | eqtr4i 2376 |
. 2
Phi Phi 0c |
46 | 1, 36, 45 | 3eqtrri 2378 |
1
Proj1 Proj2 |